I honestly thought that we were addressing the question, "What caused the cushion to be indented in the first place?" I am not seeing how this other q...
I agree that the argument presented in the OP establishes the need for an uncaused (substance) cause. However, the very next paragraph makes the state...
Because I would (understandably) assume that the cushion was previously undeformed, until the ball caused the indentation. Upon being informed that th...
Here is what you said that started us down this road. What is required to avoid an infinite regress is an event that is caused by a substance, rather ...
What are you talking about? I not only follow the argument, I agree with it. Indeed, "there must also be 'substance causation,'" but that is exactly t...
Right, the result of a cause is just what an event is. An "uncaused event" is a self-contradiction. Lots of true propositions, especially in philosoph...
That is an unwarranted assumption that is not even part of the argument as presented in the OP. In fact, it directly contradicts its very first premis...
Right, I was instead addressing the problem named in the thread title. And the original was about "the pious" and "the gods," so the common version th...
I am not addressing your argument at all, just describing the actual Euthyphro dilemma as it is commonly set forth by contemporary philosophers. It is...
Here is the actual exchange. I was correcting the mistake in the OP. You and I are in agreement here--it is false that every event is caused by anothe...
The Euthyphro is usually posed as a question: Is something good because God wills it, or does God will it because it is good? The first option makes g...
More accurately, every series of events has a first uncaused cause. Which is exactly what I said; please read more carefully. already addressed that--...
No, this would imply that every event is caused by another event, which is not what the first premiss asserts. The conclusion is that there must be a ...
Thanks for asking. The Greek word for "truth" is transliterated aletheia, so I call myself "aletheist" because I believe that there is such a thing as...
No, it is called a theorem because Gödel provided a proof; otherwise, it would be called a hypothesis or conjecture. Fermat's conjecture came to be kn...
Proof does not establish truth, it establishes justification. However, since mathematics is the science of drawing necessary conclusions about hypothe...
That would be Gödel's proof of his incompleteness theorem, and the correct term is not "unprovable" but undecidable. In this context, I am not so much...
No, the two Wikipedia quotes are not contradictory. The second one only affirms that a proof is sufficient for the truth of a proposition; it does not...
I mean exactly what I said, quoting the Stanford article--Gödel's incompleteness theorem only applies to formal systems "within which a certain amount...
This sounds like an endorsement of constructivist logic, such as intuitionistic logic, which requires a positive proof in order to affirm any proposit...
As already noted, it depends on which system of logic you have in mind, since Gödel's incompleteness theorem only applies to formal systems "within wh...
Density is irrelevant to multitude, and in any case the whole numbers are of the same multitude as the odd numbers. For any collection A that has n su...
Because the real numbers correspond to all the possible combinations of rational numbers, and therefore are necessarily of greater multitude than the ...
Mathematicians are well aware of it, and it is not a problem at all. The real numbers are of greater multitude than the rational numbers, but the even...
It depends on what you mean by "argument forms." As just pointed out, what you seem to be seeking is an axiomatization of classical logic, which typic...
Again, all the different combinations of subjects of any collection--including any infinite collection--is of greater multitude than the collection it...
No, the collection of all combinations of the subjects of a collection--even an infinite collection--is always of greater multitude than that collecti...
The mistake in the OP, going all the way back to Zeno, is thinking that discrete dimensionless positions in space and discrete durationless instants i...
As I see it, Potter and Holmes have not actually influenced anyone as real agents; those effects are more properly attributed to Rowling and Doyle, al...
It is normally parsed that way in formal logic, both modern and Aristotelian, which is the universe of discourse for this thread. In fact, the OP expl...
What J. K. Rowling and Arthur Conan Doyle have written about Harry Potter and Sherlock Holmes, respectively, is real--their books (and all derivative ...
In both modern and Aristotelian logic, every particular proposition (such as "Some B is C") is about existence in the universe of discourse. In Aristo...
Right; and in modern deductive logic, the conclusion "Some B is C" does not follow from the premises "All A is B" and "All A is C," since a universal ...
Infinite divisibility is an insufficient criterion for continuity. After all, the rational numbers are infinitely divisible--thus serving as the basis...
We have been over all of this before. Infinite divisibility is a red herring. Continuous motion through space-time is the fundamental reality. An inte...
Huh? The assumption of discreteness is what creates problems like Zeno's paradoxes. As I have said before, recognizing that continuous motion through ...
But deductive validity requires that the form must guarantee deriving only true conclusions from true premises. Right, but Aristotle stipulated that a...
I see it the other way around--measurement is arbitrary; we impose it by comparing something to a discrete unit, but the underlying reality itself is ...
Whether we are imagining them or not, the issue is whether there are any As at all. The proposition "All A is B," or equivalently "For all x, if x is ...
It seems quite evident to me that there must be a real context within which discrete things exist and react. For example, we say that they have extens...
The law of identity is "All A is A." We cannot derive "Some A is A" from that, either. Again, in modern deductive logic it is always a fallacy to deri...
Correct--we can derive "It is not the case that some A is not B" from "All A is B." However, we still cannot derive "Some A is B" from either of these...
Of course it is a concept, but the issue is whether it is "purely conceptual," as you claim. Why did it have to evolve? Because our understanding chan...
I still do not understand the question. We are discussing formal logic, what true conclusions we can--or rather, cannot--derive from that proposition,...
No, a universal proposition does not establish the universe of discourse all by itself. I provided a link, so if you want to disagree with modern cate...
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